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what is unit circle
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UNIT CIRCLE FORMULA
In mathematics, a unit circle is a circle with a radius of one. Especially in trigonometry, the unit circle is the circle of radius one centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane.
The unit circle is often denoted S1 : the generalization to higher dimensions is the unit sphere. The interior of the unit circle is called the open unit disk while the interior of the unit circle combined with the unit circle itself is called the closed unit disk.
The general equation of circle is given below:
Where (h, k) are center coordinates and r is the radius.
The unit circle formula is:
x^2 + y^2
Where x and y are the coordinate values.
SOLVED EXAMPLES UNIT CIRCLE FORMULA
Therefore P is on the unit circle.
FAQs on UNIT CIRCLE - Class 11
| 1. What is a unit circle? |  |
Ans. A unit circle is a circle with a radius of 1 unit, centered at the origin of a coordinate plane. It is often used in mathematics to understand and visualize trigonometric functions.
| 2. How is the unit circle related to trigonometry? | |
Ans. The unit circle is closely related to trigonometry as it helps in understanding the values of trigonometric functions for different angles. By considering the coordinates of points on the unit circle, we can determine the sine, cosine, and tangent values for those angles.
| 3. How can the unit circle be used to find trigonometric function values? | |
Ans. To find the trigonometric function values using the unit circle, we can consider an angle in standard position on the unit circle. The x-coordinate of the point where the terminal side intersects the unit circle represents the cosine value, and the y-coordinate represents the sine value. The tangent value can be found by dividing the sine value by the cosine value.
| 4. What are the key angles on the unit circle? | |
Ans. The key angles on the unit circle are the angles that correspond to common values of trigonometric functions. These angles include 0 degrees (or 0 radians), 30 degrees (or pi/6 radians), 45 degrees (or pi/4 radians), 60 degrees (or pi/3 radians), and 90 degrees (or pi/2 radians). Memorizing the trigonometric function values for these key angles can be helpful in solving trigonometric problems.
| 5. How can the unit circle be used to solve trigonometric equations? | |
Ans. The unit circle can be used to solve trigonometric equations by converting the equations into equations involving trigonometric function values. By applying the values of sine, cosine, and tangent for different angles on the unit circle, we can determine the solutions of the equations. The unit circle provides a visual representation of the relationship between angles and trigonometric functions, making it a useful tool in solving trigonometric problems.
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